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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.02426 |
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Table of Contents:
- Doubling measure was introduced by Beurling and Ahlfors in 1956 and now it becomes a basic concept in analysis on metric space. In this paper, for a measure which is not doubling, we introduce a notion of point-wise doubling index, and calculate the point-wise doubling indices of uniform Bernoulli measures on Bedford-McMullen carpets. As an application, we show that, except a small class of Bedford-McMullen carpets, if two Bedford-McMullen carpets are bi-Lipschitz equivalent, then they have the same fiber sequence up to a permutation.